Figure 5.

A possible mechanism for the formation of the self-organized structure. Microtubules are chemically anisotropic, growing and shrinking along the direction of their long axis. This leads to the formation of chemical trails, comprised of regions of high and low local tubulin concentration from their shrinking and growing ends respectively. These concentration trails (density fluctuations) are oriented along the direction of the microtubule. Neighboring microtubules will preferentially grow into regions in which the local concentration of tubulin is highest. When molecular transport is isotropic, microtubules grow and shrink equally in all directions, and the tubulin trails retain an isotropic distribution. For self-organization to occur, this symmetry must be broken. Gravity can do this by introducing a molecular transport term that is faster in the up-down direction. This gives rise to a slight directional bias in the formation of chemical trails. Microtubules will subsequently grow and form preferentially along the direction of these tubulin trails. These processes progressively reinforce themselves, resulting in the development of the periodic changes in microtubule orientation and concentration observed. In A, microtubules have just formed from the tubulin solution. They are still in a growing phase and have an isotropic arrangement. In B, microtubule disassembly has started to occur at the bifurcation time. This produces trails of high tubulin concentration from the shrinking ends of the microtubules. These macroscopic concentration fluctuations interact with gravity, denser fluctuations drifting downward and lighter ones upwards, leading to an anisotropy in molecular transport. In C, microtubules are growing and forming preferentially where the concentration of active tubulin is highest. Anisotropic molecular transport at the bifurcation time privileges microtubule growth along specific directions. Once started, this process subsequently mutually reinforces itself with time and leads to self-organization. When gravity is absent, molecular transport remains isotropic, and self-organization is not triggered.